Dr. Niko,
Check the network adapter cards on the Windows Ultimate machines. Make sure under the network adapter properties>power management tab is UNCHECKED (allow the computer to turn off this device to save power), so the network adapter is always on. I also agree that your "main computer/server" should NOT be allowed to go into hibernation mode.
On buying a server, buy one. It will do your network a ton of good. I have two Dell PowerEdge 2900, one I got new from Dell (approx $3,000) and one I got on Ebay that is a refurbished model (apporx $1,200). The Small Business Server 2010 operating system will cost you about $800. Hire someone to help implement the software and connect your computers to the server.
I have a feeling you will never have these connectivity issues if you have a real "server," not a "main computer" on the current peer-to-peer network. I am speaking as someone who at one time used Microsoft XP HOME edition for my office computers and Bert famously pointed out to me over and over: What is it about HOME that you don't understand?
As someone who myself struggled with the challenges of using a peer to peer network and converted to a client-server network, let me share that the client-server network is very robust and does not have these issues. It is well worth $2,000-5,000 to implement (or more depending on the hardware and I.T. support you require).
